How about changing EZE-MAD to EZE-LHR? You can fly BA and that has a great F and J product.
LAX-SCL you should fly on LAN. Very good business class, no First. But J on LAN better than F on AA.
LHR-JNB on BA.... In my opinion the J product of BA is not that much worse than F. In all honesty: I may even prefer it.
All in all after booking my AONE6 this year I decided on a DONE5 for next. I rather spend the extra money on 5 star hotels. The difference is not really worth it.